~Moving Charge Put to Use Electrical Circuits ~Moving Charge Put to Use

The Circuit All circuits, no matter how simple or complex, have one thing in common, they form a complete loop. As mentioned before, circuits should have various circuit elements in the loop. Zap! V A

Series Circuit 4 x 4 Have you ever driven down a 1 lane road? You can keep moving until… If there is an accident all traffic stops, there is no other road to follow. 4 x 4

Series Circuit A series circuit is similar to a one lane road, current can flow in only one path. Even if you add a 2nd resistor in series, there is still just 1 path. R1 R2

Series Circuit One path means all components have the same current The Voltage provided by the source must equal the Voltage drop across the resistor(s) I V R

Series Circuit One path means all components have the same current What is the voltage drop across R1? R1 I V R2

Series Circuit How do we find Req? I V Divide both sides by Is R1 Req

The Series Circuit (cont.) Every series configuration can be reduced to a single value for resistance known as the equivalent resistance, or Req. The formula for Req is as follows for series: This can be used as a step to solve for the current in the circuit or the voltage across each resistor. R1 R2 Req I

Sample Problem (Series) A circuit is configured in series as shown below. What is the equivalent resistance (Req)? What is the current through the circuit? (Hint: Use Ohm’s Law.) 10W 20W 30W 6V Ieq = 0.1A 60W 6V

Sample Problem (Series) (cont.) We still have one question to ask. What are the voltages across each resistor? For the 10W Resistor: For the 20W Resistor: For the 30W Resistor: What do you notice about the voltage sum? Voltages across resistors in series add to make up the total voltage. 10W 20W 30W 6V Ieq = 0.1A

Series Circuit Summary Current is constant throughout the entire circuit. Resistances add to give Req. Voltages across each resistor add to give Veq.

Devices that Make Use of the Series Configuration Although not practical in every application, the series connection is crucial as a part of most electrical apparatuses. Switches Necessary to open and close entire circuits. Dials/Dimmers A type of switch containing a variable resistor (potentiometer). Breakers/Fuses Special switches designed to shut off if current is too high, thus preventing fires. Ammeters Since current is constant in series, these current-measuring devices must be connected in that configuration as well. 20 20A 20A A

The Parallel Circuit (cont.) Parallel circuits are similar to rivers with branches in them. The current from the river divides into multiple paths. After the paths, the water recombines into the same amount of flowing water. Ieq I1 I2

Parallel Circuit A parallel circuit is similar to a river that branches, current can flow in multiple paths. Once the paths end, the total flow remains the same R2 R1

The Parallel Circuit Notice that the circuit branches out to each resistor, allowing multiple paths for current to flow. If there are exactly two clear paths from the ends of one resistor to the ends of the other resistor. Branch X A break in one of the branches of a parallel circuit will not disable current flow in the remainder of the circuit. Click on the circuit to animate current taking multiple paths. R1 R2

Parallel Circuit How do we find Req a parallel circuit? Use Ohm’s law Divide both sides by Vp V R1 R2 V Req V R2

The Parallel Circuit (cont.) Notice how every resistor has a direct connection to the DC source. This allows the voltages to be equal across all resistors connected this way. An equivalent resistance (Req) can also be found for parallel configurations. It is as follows: R1 R2 Req

Sample Problem (Parallel) A circuit is configured in parallel as shown below. What is the equivalent resistance of the circuit? 12W 6V 30W 60W 6V

Sample Problem (Parallel) What is the current in the entire circuit? What is the current across each resistor? The 30W Resistors The 60W Resistor 30W 60W 6V

Parallel Circuit Summary There are several facts that you must always keep in mind when solving parallel problems. Voltage is constant throughout the entire parallel circuit. The Inverses of the Resistances add to give the inverse of Req. Current through each resistor adds to give Ieq. Make use of Ohm’s Law.

Devices that Make Use of the Parallel Configuration Although not practical or safe in every application, the parallel circuit finds definite use in some electrical apparatuses. Electrical Outlets Constant voltage is a must for appliances. Light Strands Prevents all bulbs from going out when a single one burns out. Voltmeters Since voltage is constant in parallel, these meters must be connected in this way. V

Lights demo DC source with 3 lights in series DC source with 3 lights in parallel DC source with 2 lights in series 1 parallel DC source with 1 lights in series 2 parallel

Combination Circuits Some circuits have series/parallel combinations These can be reduced using equivalent resistance formulas. Now let’s solve a problem involving this circuit. Parallel R1 R2 R3 R4 Series

Sample Problem (Combo) What is the equivalent resistance (Req) of the circuit? First, we must identify the various combinations present. Series Parallel Parallel 30W 10W 20W 25V Series 10W 40W

Sample Problem (Combo) The simplified circuit only shows the equivalent resistances. Is the circuit now fully simplified? Now, we must identify the final configuration. Series 40W 10W 25V Parallel 50W 30W 10W 20W 25V Series 10W 40W

Sample Problem (Combo) The circuit is further simplified below. Can it be simplified again? Now, the circuit is completely simplified. What is the current in the entire circuit? 40W 10W 25V Series 50W 50W 25V

Combination Circuits Parallel Paths: Must make a complete loop through two resistors with out touching any other component. Series Paths: Must form a path through multiple resistors with out crossing an intersection.

Kichoff's current laws Choose a direction and label the current in each branch Identity the number of unknowns as develop as many equation Label the polarity of each Vr for all resistors. Apply Kirchoff’s junction rule (sum of current in equals sum of current out. Apply Kirchoff’s loop rule. The sum of all voltages around a loop must equal zero Solve the simultaneous equations 10W I1 I2 I3 35V 30W 1W 10W 40V 1W

Kichoff's current laws 10W 35V 30W 1W 10W 40V 1W

Make a terminal voltage slide 30W 10W 15V

25V 30W 10W 15V

24μf 12μf 36μf

113W 77W 130W 130W 151W 151W 131W 131W 117 117 W W 120W 120W 140 W 114 114 W W 220V 220V 107W 107W 44W 44W 126W 126W 113W 77W 26W 26W